[R-meta] converting Odds Ratio to Risk Ratio in CHE model

[Dr. Gerta Rücker]

Dear Sicong,

Why then were the effects transformed to SMDs in the first place? They could have been analysed as ORs (or RRs).

If you want to transform a pooled OR from a meta-analysis to an RR, you have to make an assumption of the "baseline risk" in a population which is the probability of the event of interest in the control group. If we denote the baseline risk with p_c and the risk under the active intervention with p_t, then we have

RR = p_t/p_c

OR = p_t * (1 - p_c)/ p_c / (1 - p_t)

Then, given OR and the assumed baseline risk p_c, we can solve OR for p_t:

OR * (1 - p_t) * p_c = p_t * (1 - p_c)  

Inserting this p_t into RR provides:

RR = p_t/p_c = OR /(1 +( OR - 1)* p_c)

Please note that this heavily depends on the assumption about the baseline risk, that is, on the population the intervention is thought for. This assumption should be based on evidence. See, for example, the Cochrane Handbook of Systematic Reviews for Interventions where you find similar considerations: https://training.cochrane.org/handbook/current/chapter-14#section-14-1

Best,
Gerta







UNIVERSITÄTSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta Rücker
Guest Scientist

Stefan-Meier-Straße 26 · 79104 Freiburg
gerta.ruecker using uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

-----Ursprüngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> Im Auftrag von Sicong Liu via R-sig-meta-analysis
Gesendet: Donnerstag, 18. April 2024 13:04
An: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Sicong Liu <64zone using gmail.com>
Betreff: Re: [R-meta] converting Odds Ratio to Risk Ratio in CHE model

Thank you for your response Wolfgang!

I apologize for not being clear and the question is totally motivated by making the interpreation easier. The targeted audience of the work is in public health. Although OR is  used in this domain,  some people find it difficult to think in terms of �odds", which is not as easy as �chance�  interpreted from RR, hence the question. Thank you!


Cheers,

Sicong (Zone)

-------------



From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Date: Thursday, April 18, 2024 at 6:16 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Liu Sicong <64zone using gmail.com>
Subject: RE: converting Odds Ratio to Risk Ratio in CHE model

Dear Sicong,

I don't understand the question (seems to be pattern for me today ...). If you converted everything to SMDs, then the results from the model provides estimates in terms of this (SMD) measure. So where / why do you want to convert ORs to RRs?

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Liu Sicong via R-sig-meta-analysis
> Sent: Wednesday, April 17, 2024 10:07
> To: r-sig-meta-analysis using r-project.org
> Cc: Liu Sicong <64zone using gmail.com>
> Subject: [R-meta] converting Odds Ratio to Risk Ratio in CHE model
>
> Dear All,
>
> Hope all is well.
>
> I have been applying the correlated and hierarchical model (CHE, Pustejovsky &
> Tipton, 2021) to fitting data consisting of ~98 clinical trials with binary
> outcomes. The effect sizes took the initial form of odds ratio (OR) and were
> converted to the standard mean difference (SMD) when fitting the CHE model.
> Because OR is challenging for interpretation and I wonder if there are ways to
> transform from OR to risk ratio (RR) when reporting the model parameter
> estimates? Or, as some literature (see Knol et al., 2012) suggests, converting
> to RR entails a change of model?
>
> Thank you all very much!
>
> Pustejovsky, J. E., & Tipton, E. (2022). Meta-analysis with robust variance
> estimation: Expanding the range of working models. Prevention Science, 23(3),
> 425-438.
>
> Knol, M. J., Le Cessie, S., Algra, A., Vandenbroucke, J. P., & Groenwold, R. H.
> (2012). Overestimation of risk ratios by odds ratios in trials and cohort
> studies: alternatives to logistic regression. Cmaj, 184(8), 895-899.
>
> Best regards,
> Sicong
>
> ------------------------------------------
> Sicong (Zone) Liu, Ph.D.
> Professor
> South China Normal University
> ------------------------------------------

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